Question: Determine how many solutions exist for the system of equations. ${-15x-3y = -15}$ ${y = x+3}$
Convert both equations to slope-intercept form: ${-15x-3y = -15}$ $-15x{+15x} - 3y = -15{+15x}$ $-3y = -15+15x$ $y = 5-5x$ ${y = -5x+5}$ ${y = x+3}$ Just by looking at both equations in slope-intercept form, what can you determine? ${y = -5x+5}$ ${y = x+3}$ The linear equations have different slopes. ${1}$ ${2}$ ${3}$ ${4}$ ${5}$ ${6}$ ${7}$ ${8}$ ${9}$ ${\llap{-}2}$ ${\llap{-}3}$ ${\llap{-}4}$ ${\llap{-}5}$ ${\llap{-}6}$ ${\llap{-}7}$ ${\llap{-}8}$ ${\llap{-}9}$ ${1}$ ${2}$ ${3}$ ${4}$ ${5}$ ${6}$ ${7}$ ${8}$ ${9}$ ${\llap{-}2}$ ${\llap{-}3}$ ${\llap{-}4}$ ${\llap{-}5}$ ${\llap{-}6}$ ${\llap{-}7}$ ${\llap{-}8}$ ${\llap{-}9}$ When two equations have different slopes, the lines will intersect once with one solution.